Latest developments

Here are a few recent developments........

The flexagon listing program.

Antonio's program now produces lists and state diagrams for the flexagons up to order 18. The diagrams show face numbers and direction of travel. A program to show the ministrips is also well under way. See http://www.coe.ufrj.br/~acmq/hexaflexagons. You can download the program (MSDOS).

Number of unique strips

I've implemented the algorithm to list out the unique strips. I've run it to order 18. In summary:

Order: 3 Unique strips #: 1
Order: 4 Unique strips #: 1
Order: 5 Unique strips #: 1
Order: 6 Unique strips #: 3
Order: 7 Unique strips #: 3
Order: 8 Unique strips #: 7
Order: 9 Unique strips #: 8
Order: 10 Unique strips #: 17
Order: 11 Unique strips #: 21
Order: 12 Unique strips #: 47
Order: 13 Unique strips #: 63
Order: 14 Unique strips #: 132
Order: 15 Unique strips #: 205
Order: 16 Unique strips #: 411
Order: 17 Unique strips #: 685
Order: 18 Unique strips #: 1353

I'll upload the full results later..

If you ever need to find an integer sequence try sequences@research.att.com - a blank message should give you help. It tries to match your sequence with sequences it already knows. Unhappily it is frankly baffled by the sequence for unique strips - I'll have to submit it as a new sequence, for adding to the database.

Strip and TT information.

I've written a quick applet to list (in text form) the state diagram and ministrip to build it for any Tuckerman traverse that you enter.

Enter the TT (Tuckerman traverse) in the binary form eg 010100110 (full, not abbreviated) (any rotated form acceptable) - see the theory page for details.

The list shows the TT expanded to include faces and orientations, for example:

[1a/3a]-[2b/1b*]-[4a/2a]-[1c/4c]-[2b/1b*]-[3c/2c]-

ie [topface/bottom face], a,b,c = orientation and * = 1 in the TT

The form for the ministrip is for example:

<1/3>R<2/3>L<2/1>R

ie <top face/bottom face>and R,L = direction of the path from triangle to triangle

It's not been properly tested, so use at your peril!

David King last update 19Nov01

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